Wage Rate for Output Produced

The XYZ company produces output using labor (which it purchases on an as-needed basis in the market for unskilled workers at a wage of $5 per hour) and one machine (which it is obligated to lease at a rental rate of $300 per hour ). The planning horizon precludes XYZ from renting or purchasing any additional machines, as the current machine has a capacity of 80 units of output per hour, which exceeds the projected demand for the firm's product. The firm has no alternative use for the machine it leases, and the contract precludes it from subleasing it to another party. The company currently employs one worker who produces 10 units of output per hour. A recent report from the engineering department reveals that, given the plant's current capacity, two workers could produce 20 units of output per hour, three workers could produce 30 units of output per hour, and four workers could produce a total of 40 units of output per hour.

b. Suppose XYZ can sell up to 40 units of output per hour at a price of $.60 per unit but cannot even get a penny for units produced in excess of 40 units per hour. How much output should XYZ produce each hour in order to maximize profits?

c. At what price would XYZ find it profitable to shut down its operation?